The electric discharge machine is generally used in the finishing process of various plastic forming molds, press casting molds, forging molds, etc. There are two types of the discharge finishing. The first type makes use of a discharge finishing electrode of a specific profile. The specific profile is projected on an embossed mold discharge finishing of a work piece. Thereafter, the linear discharge finishing electrode is used to effect a linear cut discharge finishing of two dimensional profile on the work piece. As far as the die-sinking mold discharge finishing is concerned, the finishing surface is a two-dimensional surface, due to the limitations of its finishing principle and the shape of the finishing electrode. As a result, it can not bring about a finishing surface which is parallel to the circumferential surface of the cylindrical work piece. In other words, the finishing surface formed on the circumferential surface of the work piece is a planar surface rather than an arcuate surface. The vertical distances between any two points of the finishing surface and the circumferential surface of the work piece are different. As a result, the finishing capability of the electric discharge machine is limited.